Semiclassical equivalence of Green-Schwarz and Pure-Spinor/Hybrid formulations of superstrings in AdS(5) x S(5) and AdS(2) x S(2) x T(6)

TL;DR

This paper proves the semiclassical equivalence of Green-Schwarz and pure-spinor superstring formulations in AdS backgrounds by comparing their one-loop partition functions and fluctuation spectra, revealing that their fermionic sectors match after accounting for ghost contributions.

Contribution

It demonstrates the equivalence of fermionic fluctuation spectra between Green-Schwarz and pure-spinor superstrings in AdS(5) x S(5), and provides evidence for similar equivalence in AdS(2) x S(2) x T(6) using specific string solutions.

Findings

Fermionic fluctuation spectra are identical in both formulations.

Extra fermionic modes cancel with pure-spinor ghosts.

Evidence supports semiclassical equivalence in multiple AdS backgrounds.

Abstract

We demonstrate the equivalence between the worldsheet one-loop partition functions computed near classical string solutions in the Green-Schwarz and in the pure-spinor formulations of superstrings in AdS(5) x S(5). While their bosonic sectors are the same in the conformal gauge, their fermionic sectors superficially appear to be very different (first vs second derivative kinetic terms, presence vs absence of fermionic gauge symmetry). Still, we show that the quadratic fluctuation spectrum of sixteen fermionic modes of the pure-spinor formulation is the same as in the Green-Schwarz superstring and the contribution of the extra "massless" fermionic modes cancels against that of the pure-spinor ghosts. We also provide evidence for a similar semiclassical equivalence between the Green-Schwarz and the hybrid formulations of superstrings in AdS(2) x S(2) x T(6) by studying several particular examples of string solutions.